Via a more direct application of the mass transference principle for
systems of linear forms [1]}, it is also
possible to prove a more general Hausdorff measure statement analogous
to the Lebesgue measure statement given by Theorem
REF . More precisely, recall that if
\(\Psi := (B_q)_{q \in {N}}\)  is a sequence of balls in \({R}^m/{Z}^m\)  and
\(n \ge 1\) , we denote by \({\cal A}_{n,m}(\Psi )\)  the set of \(\mathbf {x}\in I^{nm}\) 
such that
\(\mathbf {q}\mathbf {x}+\mathbf {p}\in B_{|\mathbf {q}|}\) 
